Risk-Sensitive Asset Management in a Wishart-Autoregressive Factor Model with Jumps

Hata, Hirofumi; Sekine, Jun

doi:10.1007/s10690-017-9231-4

Cited by 6 publications

(7 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[17,18,7,8]) and portfolio optimization (cf. [6,22]) in multi-variate stochastic volatility models. Wishart processes, taking values in the space of positive definite matrices S d ++ , are multivariate generalizations of the square root Bessel diffusion.…”

Section: Given An Open Domain E ⊆ R D and Functionsmentioning

confidence: 99%

Large Time Behavior of Solutions to SemiLinear Equations with Quadratic Growth in the Gradient

Robertson¹,

Xing²

2015

SIAM J. Control Optim.

View full text Add to dashboard Cite

This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. LARGE TIME BEHAVIOR OF SOLUTIONS TO SEMI-LINEAR EQUATIONS WITH QUADRATIC GROWTH IN THE GRADIENT SCOTT ROBERTSON AND HAO XINGAbstract. This paper studies the large time behavior of solutions to semi-linear Cauchy problems with quadratic nonlinearity in gradients. The Cauchy problem considered has a general state space and may degenerate on the boundary of the state space. Two types of large time behavior are obtained: i) pointwise convergence of the solution and its gradient; ii) convergence of solutions to associated backward stochastic differential equations. When the state space is R d or the space of positive definite matrices, both types of convergence are obtained under growth conditions on coefficients. These large time convergence results have direct applications in risk sensitive control and long term portfolio choice problems.

show abstract

Section: Given An Open Domain E ⊆ R D and Functionsmentioning

confidence: 99%

Large Time Behavior of Solutions to SemiLinear Equations with Quadratic Growth in the Gradient

Robertson¹,

Xing²

2015

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…We briefly mention more recent studies related to continuous-time portfolio optimization. (i) Regarding objective functions, we list some studies: the risk-sensitive criterion [HS17]; the conditional value-at-risk (or expected shortfall) [MY17]; the power utility [ET08]; and the exponential utility [MZ19]. (ii) The mean-variance portfolio optimization has been also investigated in the continuous-time setting.…”

Section: Introductionmentioning

confidence: 99%

Continuous-time Portfolio Optimization for Absolute Return Funds

Ieda¹

2021

Preprint

View full text Add to dashboard Cite

This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance criterion based on the lower mean square error between the investor's wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton-Jacobi-Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper.

show abstract

“…In this article, long run optimal investment and portfolio turnpike problems are studied in a multi-asset factor model where the state variable takes values in the space of positive definite matrices. Such models generalize the Wishart model of [8,27] (amongst many others), which has been successfully employed in a wide-range of problems in Mathematical Finance. In addition to identifying optimal long run policies and proving turnpike theorems, we are particularly concerned with connecting the finite horizon and long run problems.…”

Section: Introductionmentioning

confidence: 99%

“…Our results confirm this observation. In [27], the portfolio optimization problem is solved in the Wishart case via a matrix Riccati differential equation. In [2], logarithmic utility is studied, and in [42] the indifference pricing is discussed.…”

Section: Introductionmentioning

confidence: 99%

“…Proposition 3.2 provides simple, mild (especially in the case where the investor risk aversion exceeds that of a logarithmic investor) parameter restrictions under which the main results follow. Proposition 3.3 explicitly identifies the long-run limit policy when the model is further specified to the "classical" affine Wishart model considered in [8,27] and Example 3.4 constructs the non exponentially affine counter example. After considering the Wishart case, the main results for general matrix valued state variables are given in Section 3.2 : see Theorem 3.10 for the long run limit results and Theorem 3.12 for the turnpike results.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Long-Term Optimal Investment in Matrix Valued Factor Models

Robertson¹,

Xing²

2017

SIAM J. Finan. Math.

View full text Add to dashboard Cite

Abstract. Long horizon optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approaches infinity. Additionally, portfolio turnpikes are obtained in which finite horizon optimal strategies for general utility functions converge to the long-run optimal strategy for isoelastic utility. By using results on large time behavior of semilinear partial differential equations, our analysis extends, to a nonaffine setting, affine models where the Wishart process drives investment opportunities.

show abstract

Risk-Sensitive Asset Management in a Wishart-Autoregressive Factor Model with Jumps

Cited by 6 publications

References 31 publications

Large Time Behavior of Solutions to SemiLinear Equations with Quadratic Growth in the Gradient

Large Time Behavior of Solutions to SemiLinear Equations with Quadratic Growth in the Gradient

Continuous-time Portfolio Optimization for Absolute Return Funds

Long-Term Optimal Investment in Matrix Valued Factor Models

Contact Info

Product

Resources

About